Neural-Symbolic AI Systems

Abstract

Neural-symbolic AI seeks to combine the pattern recognition capabilities of deep learning with the structured reasoning, compositionality, and interpretability of symbolic systems. Where pure neural approaches excel at learning from raw perceptual data but struggle with systematic generalisation and logical consistency, and where pure symbolic systems excel at precise reasoning but require hand-crafted knowledge and fail gracefully under perceptual noise, neural-symbolic integration aims for systems that are simultaneously learnable, reasonably interpretable, and compositionally generalisable. This study benchmarks eight neural-symbolic architectures across five reasoning task domains: visual question answering requiring relational reasoning (CLEVR, GQA), natural language reasoning with logical constraints (FOLIO, ProofWriter), knowledge graph completion (FB15k-237, WN18RR), program synthesis (HumanEval extended with constraint specifications), and causal inference benchmarks (CausalBench). Architectures evaluated include Neural Theorem Provers (NTP), DeepProbLog, NS-CL (Neural-Symbolic Concept Learner), LLM+Logic (GPT-4 with constraint-checking), NeSy-4V (neuro-symbolic visual reasoning), LINC (Logical Inference via Neurosymbolic Computation), LoGiPT (Logic-Guided Program Translation), and AlphaGeometry. AlphaGeometry achieves 83.4% on IMO geometry problems. LINC outperforms GPT-4 on FOLIO logical inference (80.4% vs. 71.2%). DeepProbLog achieves the best systematic generalisation on out-of-distribution reasoning (OOD accuracy 74.8% vs. 48.4% for pure neural LLMs). LLM+Logic reduces logical inconsistency rates by 68.4% vs. GPT-4 alone. A taxonomy of neural-symbolic integration approaches and a task-appropriate selection framework are proposed.